If you owe debt to a debt collection agency the debt collector can chase the debt and chase you for the debt for as long as they want too.
However the debt collector cannot sue you or legally force you to pay the debt back after 7 years have passed and they haven't sued you yet.
If you cannot pay the debt collector back the best thing to do is to not respond to the debt collector because if you do and agree to make payments and fail to make those payments then the clock will begin again and it will be longer until the debt collector can no longer force you to pay the debt.
After 7 years the debt is usually written off your credit report and no longer affects your credit score.
However sometimes you may need to get a credit repair agency involved to repair your credit and remove the negative remarks from your credit score and credit rating.